Statement I: An elevator can go up or down with uniform speed when its weight is balanced with the tension of its cable. [2023]

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Q.
Given below are two statements:

Statement I: An elevator can go up or down with uniform speed when its weight is balanced with the tension of its cable.

Statement II: Force exerted by the floor of an elevator on the foot of a person standing on it is more than his/her weight when the elevator goes down with increasing speed.

In the light of the above statements, choose the correct answer from the options given below: [2023]

1 Statement I is false but Statement II is true

2 Statement I is true but Statement II is false

3 Both Statement I and Statement II are false

4 Both Statement I and Statement II are true

Ans.
(2)

$Statement-1$

When elevator is moving with uniform speed, $T = F_{g}$

$Statement-2$

When elevator is going down with increasing speed, its acceleration is downward.

$Hence W - N = \frac{W}{g} \times a$

$N = W (1 - \frac{a}{g}), i.e., less than weight.$

Solution

1 Statement I is false but Statement II is true

2 Statement I is true but Statement II is false

3 Both Statement I and Statement II are false

4 Both Statement I and Statement II are true

Ans.
(2)

$Statement-1$

When elevator is moving with uniform speed, $T = F_{g}$

$Statement-2$

When elevator is going down with increasing speed, its acceleration is downward.

$Hence W - N = \frac{W}{g} \times a$

$N = W (1 - \frac{a}{g}), i.e., less than weight.$

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Solution

1 Statement I is false but Statement II is true

2 Statement I is true but Statement II is false

3 Both Statement I and Statement II are false

4 Both Statement I and Statement II are true

Ans. (2) Statement-1 When elevator is moving with uniform speed, T=Fg Statement-2 When elevator is going down with increasing speed, its acceleration is downward. Hence W-N=Wg×a N=W(1-ag), i.e., less than weight.

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Ans.
(2)

$Statement-1$

When elevator is moving with uniform speed, $T = F_{g}$

$Statement-2$

When elevator is going down with increasing speed, its acceleration is downward.

$Hence W - N = \frac{W}{g} \times a$

$N = W (1 - \frac{a}{g}), i.e., less than weight.$